Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory

2011 ◽  
Vol 225 (2) ◽  
pp. 498-506 ◽  
Author(s):  
M Mohammadimehr ◽  
A R Saidi ◽  
A Ghorbanpour Arani ◽  
A Arefmanesh ◽  
Q Han
Keyword(s):  
Elastic Medium ◽  
Axial Compression ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Small Scale ◽  
Beam Model ◽  
Critical Buckling Load ◽  
Non Local ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Using the non-local elasticity theory, Timoshenko beam model is developed to study the elastic buckling of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium under axial compression. The non-local effects in the normal and transverse shear stress components are considered. The effects of the surrounding elastic medium based on a Winkler model and van der Waals' (vdW) force between the inner and outer nanotubes are taken into account. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling loads under axial compression are obtained. The numerical results are reported using the non-local Timoshenko beam theory and compared with those obtained using the non-local Euler—Bernoulli beam theory. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. Furthermore, in order to estimate the non-local critical buckling load of DWCNTs under axial compression, a simplified analysis is carried out and the results are compared with those obtained using molecular mechanics.

Thermal buckling analysis of double-walled carbon nanotubes considering the small-scale length effect

2011 ◽  
Vol 225 (1) ◽  
pp. 248-256 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
M Mohammadimehr ◽  
A R Saidi ◽  
S Shogaei ◽  
A Arefmanesh
Keyword(s):  
Temperature Change ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Small Scale ◽  
Buckling Mode ◽  
Critical Buckling Load ◽  
Winkler Model ◽  
Non Local ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this article, the buckling analysis of a double-walled carbon nanotube (DWCNT) subjected to a uniform internal pressure in a thermal field is investigated. The effects of the temperature change, the surrounding elastic medium based on the Winkler model, and the van der Waals forces between the inner and the outer tubes are considered using the continuum cylindrical shell model. The small-length scale effect is also included in the present formulation. The results show that there is a unique buckling mode corresponding to each critical buckling load. Moreover, it is shown that the non-local critical buckling load is lower than the local critical buckling load. It is concluded that, at low temperatures, the critical buckling load for the infinitesimal buckling of a DWCNT increases as the magnitude of temperature change increases whereas at high temperatures, the critical buckling load decreases with the increasing of the temperature.

Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory

2020 ◽  
Vol 62 ◽  
pp. 108-119
Author(s):  
Tayeb Bensattalah ◽  
Ahmed Hamidi ◽  
Khaled Bouakkaz ◽  
Mohamed Zidour ◽  
Tahar Hassaine Daouadji
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Axial Compression ◽  
Buckling Load ◽  
Small Scale ◽  
Beam Model ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Nonlocal Continuum Theory ◽  
Walled Carbon Nanotubes

The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.

Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model

2015 ◽  
Vol 5 (3) ◽  
pp. 209-221 ◽  
Author(s):  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Variational Principles ◽  
Linear Time ◽  
Scale Effects ◽  
Time Dependent ◽  
Small Scale ◽  
Beam Model ◽  
Geometric Boundary ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

AbstractVariational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

Vibration of Double-Walled Carbon Nanotube-Based Mass Sensor via Nonlocal Timoshenko Beam Theory

2011 ◽  
Vol 2 (3) ◽  
Author(s):  
Zhi-Bin Shen ◽  
Bin Deng ◽  
Xian-Fang Li ◽  
Guo-Jin Tang
Keyword(s):  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Tube Length ◽  
Beam Model ◽  
Mass Sensor ◽  
Nonlocal Timoshenko Beam Theory ◽  
Double Walled Carbon Nanotubes ◽  
Tip Mass

The potential of double-walled carbon nanotubes (DWCNTs) as a micromass sensor is explored. A nonlocal Timoshenko beam carrying a micromass at the free end of the inner tube is used to analyze the vibration of DWCNT-based mass sensor. The length of the outer tube is not equal to that of the inner tube, and the interaction between two tubes is governed by van der Waals force (vdW). Using the transfer function method, the natural frequencies of a nonlocal cantilever with a tip mass are computed. The effects of the attached mass and the outer-to-inner tube length ratio on the natural frequencies are discussed. When the nonlocal parameter is neglected, the frequencies reduce to the classical results, in agreement with those using the finite element method. The obtained results show that increasing the attached micromass decreases the natural frequency but increases frequency shift. The mass sensitivity improves for short DWCNTs used in mass sensor. The nonlocal Timoshenko beam model is more adequate than the nonlocal Euler-Bernoulli beam model for short DWCNT sensors. Obtained results are helpful to the design of DWCNT-based resonator as micromass sensor.

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